Question
Mathematics Question on mathematical reasoning
Negation of the Boolean statement (p ∨ q) ⇒ ((~ r) ∨ p) is equivalent to
A
p ∧ (~ q) ∧ r
B
(~ p) ∧ (~ q) ∧ r
C
(~p) ∧ q ∧ r
D
p ∧ q ∧ (~ r)
Answer
(~p) ∧ q ∧ r
Explanation
Solution
The correct answer is (C) : (p) ∧ q ∧ r r ∨ p)
p ∨ q ⇒ (
≡ ~ (p ∨ q) ∨ (~ r ∨ p)
≡ (~ p ∧ ~ q) ∨ (p ∨ ~ r)
≡ [(~ p ∨ p) ∧ (~ q ∨ p)] ∨ ~ r
≡ (~ q ∨ p) ∨ ~ r
Its negation is ~ p ∧ q ∧ r.